Block #292,970

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 1:26:35 AM · Difficulty 9.9905 · 6,510,917 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

e3b8e86bdc638cafeeb3981530b7440e59929656690ec2b4474bb984bb2295ac

View on Chainz ↗

Height

#292,970

Difficulty

9.990458

Transactions

Size

725 B

Version

Bits

09fd8ea7

Nonce

28,569

Timestamp

12/4/2013, 1:26:35 AM

Confirmations

6,510,917

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

81b2b9c74176a19aa7a5aba10d4bc3075bf41f77932b22b630ab1f24f8f17bfa

Transactions (2)

Coinbasec967df151a3f2a…fb5fab753f24eb

1 in → 1 out10.0100 XPM110 B

AeKNrjNj…1NEq95Ta

aaf2d53c758b31…c638dd36a1cd6f

3 in → 2 out2.1047 XPM525 B

ALSB9RGy…tkrjehDq AUGEPHyf…yfJpLed8

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.884 × 10⁹³(94-digit number)

88841295638831586437…64013456203238252799

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

8.884 × 10⁹³(94-digit number)

88841295638831586437…64013456203238252799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.884 × 10⁹³(94-digit number)

88841295638831586437…64013456203238252801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.776 × 10⁹⁴(95-digit number)

17768259127766317287…28026912406476505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.776 × 10⁹⁴(95-digit number)

17768259127766317287…28026912406476505601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.553 × 10⁹⁴(95-digit number)

35536518255532634575…56053824812953011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.553 × 10⁹⁴(95-digit number)

35536518255532634575…56053824812953011201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.107 × 10⁹⁴(95-digit number)

71073036511065269150…12107649625906022399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.107 × 10⁹⁴(95-digit number)

71073036511065269150…12107649625906022401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.421 × 10⁹⁵(96-digit number)

14214607302213053830…24215299251812044799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.421 × 10⁹⁵(96-digit number)

14214607302213053830…24215299251812044801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer